Abstract: An implantation prosthesis, and a composite material for use in constructing this prosthesis. The material is flexible. It has an inner wall, an outer wall, and a foam layer between the walls in adherent surface-to-surface contact. The walls are made of a flexible elastomeric material with at least limited permeability. The foam is resiliently deformable to resist sharp folding of the walls, and to resist relative in-plane motion of the walls.